{
  "annotation_id": "a11b484c-8775-43cf-b681-3a89a9ba5e57",
  "date_created": "2026-03-02T18:01:49.452000Z",
  "date_modified": "2026-03-02T18:01:49.452000Z",
  "file_hash": "c50690600935c7f2aa0125bc37d3bd62af5daaa768a5457042e37e8630621c28",
  "private": false,
  "record": {
    "abstract": "We study the three-body Coulomb problem in two dimensions and show how to\ncalculate very accurately its quantum properties. The use of a convenient set\nof coordinates makes it possible to write the Schr\\\"{o}dinger equation only\nusing annihilation and creation operators of four harmonic oscillators, coupled\nby various terms of degree up to twelve. We analyse in details the discrete\nsymmetry properties of the eigenstates. The energy levels and eigenstates of\nthe two-dimensional helium atom are obtained numerically, by expanding the\nSchr\\\"{o}dinger equation on a convenient basis set, that gives sparse banded\nmatrices, and thus opens up the way to accurate and efficient calculations. We\ngive some very accurate values of the energy levels of the first bound Rydberg\nseries. Using the complex coordinate method, we are also able to calculate\nenergies and widths of doubly excited states, i.e. resonances above the first\nionization threshold. For the two-dimensional $H^{-}$ ion, only one bound state\nis found.",
    "arxiv_id": "quant-ph/0203150",
    "authors": [
      "L. Hilico",
      "B. Gr\u00e9maud",
      "T. Jonckheere",
      "N. Billy",
      "D. Delande"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.022101",
    "title": "Quantum three body Coulomb problem in two dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0203150"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2ae3d824-c46a-405f-b777-621f490ab432",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}